A)
1 answer:
Given:
The boundary line of an inequality is:
The solution set contains (0,0).
To find:
The inequality.
Solution:
The boundary line of an inequality is
Since (0,0) is in the solution set, therefore (0,0) satisfies the required inequality.
Taking LHS, we get
Substitute x=0 and y=0.
The right hand side of the given equation is 6.
We know that,
The boundary line is not a dotted line, it means the points on the boundary line are also included in the solution set. So, the inequality sign must be .
Therefore, the required inequality is .
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- Vertex form:
So firstly, put x^2 - 4x into parentheses:
Next, we need a perfect square inside the parentheses. Divide the x coefficent by 2 then square that result. In this case, -4 ÷ 2 = -2, (-2)²= 4. Add 4 inside the parentheses and then subtract 4 outside the parentheses:
Lastly, factor what's inside the parentheses and <u>your vertex form is </u>
Option A: The rate of change of Function R is less than the rate of change of Function S because is true.
Explanation:
The function
The equation for function R can be determined using the slope formula,
The y-intercept is the value of y, when x = 0.
Thus, the y-intercept is .
To determine the slope, let us substitute the coordinates and
.
Because, the points on the straight line have the same slope.
Thus, we have,
Thus, and
Let us substitute these values in the formula , we get,
Hence, the equation of R is
The equation of S is
Comparing the slope of these two equations, we have,
This means that the slope of R is less than the slope of S.
Hence, The rate of change of Function R is less than the rate of change of Function S because
Thus, Option A is true.